MRI Physics: Spin Echo and Gradient Echo

1) 90° creates coherent Mxy.
2) During τ, spins in a slightly stronger field run ahead, weaker ones lag.
3) 180° flips the phase order: the fast spins are now behind.
4) Same speeds as before, so the fast spins catch up.
5) All realign at TE = 2τ → echo.
Like runners who all turn around at a whistle and arrive back at the start line together.

It refocuses dephasing from static field differences (B0 inhomogeneity, susceptibility, chemical shift); it cannot undo random T2 processes.
So SE echo amplitude decays with T2, not T2*. Only effects that are identical before and after the 180° cancel; random fluctuations, diffusion and flow do not.

One gradient lobe deliberately dephases the spins by position; a reversed lobe of equal area rephases them. The echo appears when the net gradient area is back to zero.
No 180° RF pulse is involved.

Only the dephasing caused by its own gradient. Static B0 inhomogeneity keeps dephasing, so GRE amplitude decays with T2*.
That is why GRE is sensitive to susceptibility (air bubbles, tissue–air boundaries) and visibly improves after shimming.

GRE: no 180°, small flip angles possible → short TE/TR, fast, but T2*-sensitive. SE: the 180° recovers static dephasing → robust signal and true T2 contrast, but slower and more RF power (SAR).

TE = time from excitation to echo centre (how long Mxy decays before you measure). TR = time between successive excitations of the same slice (how long Mz recovers).
TE controls T2/T2* weighting; TR controls T1 weighting.

S ∝ ρ · (1 − e^(−TR/T1)) · e^(−TE/T2).
Read it left to right: how many protons × how much Mz recovered during TR × how much Mxy survives until TE. TR only acts on the T1 factor, TE only on the T2 factor. (Assumes 90° pulses and TR ≫ TE.)

Short TR and short TE.
Short TR catches tissues at different stages of recovery, so short-T1 tissue is brighter. Short TE keeps T2 differences from adding competing contrast. "Short" and "long" are relative to the tissue's T1 and T2.

Long TR and long TE.
Long TR lets every tissue recover (removes T1 differences). Long TE lets long-T2 tissue keep more signal than short-T2 tissue, so fluid is bright.

Long TR and short TE.
Long TR removes T1 differences, short TE removes T2 differences, so brightness mainly reflects the number of protons.

It mixes T1 and T2 weighting, which tend to cancel, and leaves little signal.
In tissue, long T1 usually goes with long T2: short TR makes long-T1 tissue dark while long TE makes long-T2 tissue bright, so the effects fight.

No. Long TR only removes T1 contrast; without a long TE the result is proton-density weighted.

T1w: WM brightest, GM grey, CSF dark. T2w: CSF bright, GM brighter than WM.
CSF has very long T1 (barely recovers at short TR → dark on T1w) and very long T2 (keeps signal at long TE → bright on T2w). Tutorial values at 1.5 T: WM 600/80 ms, GM 900/100 ms, CSF 3500/2000 ms (T1/T2).

They depend on the molecular environment: how freely water tumbles and what it interacts with.
Different tissues therefore relax at different rates, and the acquisition timing decides which difference shows up as brightness.

After enough identical repetitions, the magnetization at the same point of every TR is the same from cycle to cycle.
At short TR this steady Mz is much smaller than M0. The first few cycles differ, so "dummy" repetitions are often run before recording.

The flip angle that maximises steady-state signal for a given TR and T1: cos θ_E = e^(−TR/T1).
At short TR, 90° pulses would saturate; a smaller angle uses less Mz each time but leaves more for the next pulse. Example: T1 = 600 ms, TR = 20 ms → θ_E ≈ 14.7°. At long TR → 90°.

To get the most signal (SNR) per unit time in fast, short-TR imaging or spectroscopy.
It is the best compromise between "tip a lot now" and "keep Mz for the next pulse".

No. Contrast needs the largest signal difference between two tissues, not the largest single signal.
Tutorial (TR = 20 ms, T1 = 600 vs 900 ms): Ernst angle for WM ≈ 14.7°, best WM–GM CNR ≈ 23°. Going from 14.7° to 20° lowered SNR but raised CNR.

It reduces it, with a similar effect to a long TR.
Little Mz is used per pulse, so all tissues stay close to full recovery and look alike. The tutorial used TR = 200 ms with ~13° to remove T1 contrast before adding T2 weighting with TE.

SNR = signal / noise SD: how visible one tissue is. CNR = |S_A − S_B| / noise SD: how distinguishable two tissues are.
Worked: signals 100 and 95, noise 5 → SNR 20 and 19, but CNR = 1. Both tissues are clearly visible, yet their boundary is not.
Trap: a bright image is not automatically a high-contrast image.

More signal per repetition, but T1 contrast shrinks once both tissues are nearly recovered, and scan time grows in proportion to TR.
So CNR does not keep rising with TR.

Less signal, so the image looks noisier, while T2 contrast first grows and then both signals sink toward the noise.
CNR therefore peaks at an intermediate TE (≈ 100 ms in the tutorial, with a broad optimum). Changing TE does not change the tissue's T2.

TE must fit inside TR, so a long TE forces a long TR, and scan time ∝ TR × number of lines.
Tutorial: 24,576 lines take ~8 min at TR = 20 ms, ~7 h at TR = 1 s; TR = 200 ms for T2w gave > 80 min. Real T2w scans use faster methods (e.g., turbo spin echo).

TI sets how far each tissue's Mz has recovered from −M0 when the excitation arrives.
Tissues with different T1 sit at different points on their recovery curves (some still negative, some crossing zero, some positive) at the same TI, so TI picks the contrast. TE then picks a point on the transverse decay.

When the excitation arrives exactly as its Mz crosses zero: there is nothing to tip, so no signal.
After a full inversion from equilibrium, TI_null = T1·ln 2 ≈ 0.69·T1. Incomplete recovery (finite TR) makes the null earlier: tutorial WM (T1 600 ms, TR 1 s) ≈ 300–325 ms instead of 416 ms. The protons are still there.

Fluid-attenuated inversion recovery: TI is chosen to null CSF (very long T1), usually combined with T2 weighting.
Result: T2 contrast with dark fluid, so lesions next to CSF stand out.

Magnitude images throw away the sign, so negative Mz looks as bright as positive Mz.
Brightness falls to zero at each tissue's null and rises again. Equal brightness happens once when both are negative with equal size and once when they have opposite signs. Tutorial (TR 1 s, 40°): WM = GM near 190–200 ms and near 335 ms.

Contrast barely changes: the 180° inversion still sets the T1 contrast.
Any pulse α leaves Mz_after = Mz_before·cos α, so 40° keeps ≈ 77% of Mz instead of destroying it; the recovery curve just shows a smaller jump at the excitation.

Use T2 weighting: first remove T1 contrast (long TR or small flip angle), then lengthen TE so the different T2 values separate while signal stays above noise.

Equal proton density is assumed, so WM ≈ GM; CSF (T1 ≈ 3500 ms) has not fully recovered in 8 s.
Long TR + short TE removes T1 and T2 contrast (PD weighting), but "long" must be long compared with the longest T1: full recovery needs ≈ 5·T1 ≈ 17.5 s for CSF.